Jought in the clan except few lengrage over $\{a,b\}(15)$

$(1)$ Larguage accepting strings of length exacty $2.$

Larguage accepting strings of longth at thent $2$

$(3)$ Language accepting strings of longh at most

$(2)$ Convert the following Regular Exportion to ther equivaleat finite automata

$(1)6a**b$

$(2)(a+b)c(15)$

$($b$)a(bc{)}^{**}$

$(4)(b(a^{+}b|)|)$

$(3)$ Convert the following Regular Expression to its equivalent Finte Aubomata.

$10+(0+11)0^{**}$

$(4)$ Show shat

$(a+b{)}^{**}=(a^{**}+b^{**})(5)$

$(5)$ Explain the following question and $(10)$

Design a Regular expression for

$($a$)$ Contain a substring aab

Ans: $(a+b{)}^{**}$aab$(a+b{)}^{**}$

$($b$)$ Starts and ends with a An: $a+a(a+b{)}^{**}a$

$($c$)$ Starts and ends with same symbes

AM$)a+a(a+b{)}^{**}a+b+b(a+b{)}^{**}b$

$($d$)$ Starts and ends wim different.

ny$)a(a+b{)}^{**}b+b(a+b{)}^{**}a$

$($c$)||=3$

A

$($f$)||3$

$ sy

$ $||3$

$$

$($a$)|{|}_a=2$

$$

$(1)|w{|}_{a}2$

Ans

$(1)3^s$ Spubir from left end is $6.$

$$

$(6)$ Consider the following langrage $L_1=$ and $L_2=\{1\}$ which ove of the follming represent $L_1^{**}{L}_1^{**}{L}_2^{**}?(5)$